title: Statistical strategies for constructing health risk models with multiple pollutants and their interactions: possible choices and comparisons.
abstract: BACKGROUND
  As public awareness of consequences of environmental exposures has grown, estimating the adverse health effects due to simultaneous exposure to multiple pollutants is an important topic to explore. The challenges of evaluating the health impacts of environmental factors in a multipollutant model include, but are not limited to: identification of the most critical components of the pollutant mixture, examination of potential interaction effects, and attribution of health effects to individual pollutants in the presence of multicollinearity.
  
  
  METHODS
  In this paper, we reviewed five methods available in the statistical literature that are potentially helpful for constructing multipollutant models. We conducted a simulation study and presented two data examples to assess the performance of these methods on feature selection, effect estimation and interaction identification using both cross-sectional and time-series designs. We also proposed and evaluated a two-step strategy employing an initial screening by a tree-based method followed by further dimension reduction/variable selection by the aforementioned five approaches at the second step.
  
  
  RESULTS
  Among the five methods, least absolute shrinkage and selection operator regression performs well in general for identifying important exposures, but will yield biased estimates and slightly larger model dimension given many correlated candidate exposures and modest sample size. Bayesian model averaging, and supervised principal component analysis are also useful in variable selection when there is a moderately strong exposure-response association. Substantial improvements on reducing model dimension and identifying important variables have been observed for all the five statistical methods using the two-step modeling strategy when the number of candidate variables is large.
  
  
  CONCLUSIONS
  There is no uniform dominance of one method across all simulation scenarios and all criteria. The performances differ according to the nature of the response variable, the sample size, the number of pollutants involved, and the strength of exposure-response association/interaction. However, the two-step modeling strategy proposed here is potentially applicable under a multipollutant framework with many covariates by taking advantage of both the screening feature of an initial tree-based method and dimension reduction/variable selection property of the subsequent method. The choice of the method should also depend on the goal of the study: risk prediction, effect estimation or screening for important predictors and their interactions.
authors.affiliation: Department of Biostatistics, University of Michigan School of Public Health, Ann Arbor, MI USA. zcs@umich.edu.
authors.forename: Zhichao
authors.initials: Z
authors.lastname: Sun
authors.forename: Yebin
authors.initials: Y
authors.lastname: Tao
authors.forename: Shi
authors.initials: S
authors.lastname: Li
authors.forename: Kelly K
authors.initials: KK
authors.lastname: Ferguson
authors.forename: John D
authors.initials: JD
authors.lastname: Meeker
authors.forename: Sung Kyun
authors.initials: SK
authors.lastname: Park
authors.forename: Stuart A
authors.initials: SA
authors.lastname: Batterman
authors.forename: Bhramar
authors.initials: B
authors.lastname: Mukherjee
mesh_terms: D000293:Adolescent; D000328:Adult; D000368:Aged; D000369:Aged, 80 and over; D000393:Air Pollutants / Q000633:toxicity*; D002648:Child; D004781:Environmental Exposure; D004784:Environmental Monitoring / Q000379:methods*; D005260:Female; D006801:Humans; D008297:Male; D008875:Middle Aged; D008954:Models, Biological; D018570:Risk Assessment / Q000379:methods; D055815:Young Adult
chemical_list: D000393:Air Pollutants